Who invented Spherical lens
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DA "spherical lens" is a lens whose surface has the shape of (part of) the surface of a sphere. On this page, we will determine some values for the focal length of a spherical lens.
Figure 1 -- Spherical Aberration
A spherical lens doesn't actually bring parallel rays to a common focus (see figure 1). Rather, the "focus" of the lens depends on the distance from the distance from the center of the lens, with light passing through the edges of the lens coming to a focus closer to the lens than light passing through the center. This produces the phenomenon of "focus shift", which is well known to photographers: If your lens suffers from severe "focus shift", and you focus the image with the diaphragm wide open, and then stop down to take the picture, the picture won't be in focus. With the lens opened wide the image is dominated by light passing through the lens far from the center; consequently, it's the edge rays which you've adjusted the lens to bring to a sharp focus. The center rays, on the other hand, are coming to a focus behind the film plane; when the lens is stopped down, only those (out of focus) center rays are left.
On the remainder of this page, we'll find an exact formula for the focal length of a spherical lens, and we'll then find an approximate formula for the focal length at the center of the lens. This problem is somewhat messy, and we're going to break the problem down into easier to handle pieces by cutting the lens in half. We'll find the focal length of each half lens and then put them together to get the focal length of a convex-convex spherical lens.
Figure 1 -- Spherical Aberration
A spherical lens doesn't actually bring parallel rays to a common focus (see figure 1). Rather, the "focus" of the lens depends on the distance from the distance from the center of the lens, with light passing through the edges of the lens coming to a focus closer to the lens than light passing through the center. This produces the phenomenon of "focus shift", which is well known to photographers: If your lens suffers from severe "focus shift", and you focus the image with the diaphragm wide open, and then stop down to take the picture, the picture won't be in focus. With the lens opened wide the image is dominated by light passing through the lens far from the center; consequently, it's the edge rays which you've adjusted the lens to bring to a sharp focus. The center rays, on the other hand, are coming to a focus behind the film plane; when the lens is stopped down, only those (out of focus) center rays are left.
On the remainder of this page, we'll find an exact formula for the focal length of a spherical lens, and we'll then find an approximate formula for the focal length at the center of the lens. This problem is somewhat messy, and we're going to break the problem down into easier to handle pieces by cutting the lens in half. We'll find the focal length of each half lens and then put them together to get the focal length of a convex-convex spherical lens.
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Between the 11th and 13th century "reading stones" were invented. Often used by monks to assist in illuminating manuscripts, these were primitive plano-convex lenses initially made by cutting a glass sphere in half.
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